-LRB- CNN -RRB- -- The ex-wife of a Texas convict executed in 2004 for the deaths of his three children reaffirmed her belief in his guilt Wednesday as his relatives sought to open a new inquiry into the case .

The family of Cameron Todd Willingham has asked a judge to posthumously clear his name , arguing that he was put to death based on `` junk science . '' Though Willingham was executed in 2004 for killing his three daughters by setting fire to his house , subsequent investigations by outside experts have concluded that the fire that killed the girls should not have been ruled arson .

Willingham 's ex-wife , Stacy Kuykendall , has kept a low profile throughout the debate over his execution . But she told reporters outside the Travis County courthouse in Austin that `` I am here to make sure that my daughters ' voices are heard . ''

`` Todd murdered Amber , Karmon and Kameron . He burnt them , '' she said . `` He admitted he burnt them to me , and he was convicted for his crime . That is the closest to justice that my daughters will ever get . ''

Kuykendall spoke before an Austin judge opened a hearing into the Willingham 's family 's request for an inquiry into the execution . But inside the courtroom , prosecutors from the town of Corsicana -- where the 1991 fire took place -- forced a delay in the proceedings by challenging the impartiality of District Judge Charlie Baird and asking him to recuse himself .

Baird told lawyers he will issue a decision on that request next week , said Gerry Goldstein , a lawyer representing Willingham 's stepmother , Eugenia Willingham , and cousin Patricia Cox .

Goldstein pointed out that Kuykendall has told differing stories about whether her former husband ever admitted his guilt in the fatal fire , and criticized death-penalty supporters for `` parading her on the courthouse steps while they 're inside trying to stop proceedings . ''

`` What possible harm could there be to their side to have this aired in court ? '' he asked .

Also representing the family is The Innocence Project , led by nationally known defense lawyer Barry Scheck . Lowell Thompson , the district attorney for Navarro County , which includes Corsicana , did not return a phone call seeking comment Wednesday .

In asking Baird to open a `` court of inquiry '' into the execution , Willingham 's family argues that he was put to death for a crime `` that modern science reveals may never have been committed . '' State officials failed to act on evidence of `` significant deficiencies '' in the finding of arson at the heart of the case before the execution , and have `` continued to resist attempts to clear Mr. Willingham 's name , '' their petition states .

`` If we can get a hearing before him or any other fair judge , we 're going to go ahead , '' Goldstein said .

The Texas Forensic Science Commission is investigating claims that state fire marshals ruled the fatal blaze arson based on outdated or faulty science . The first of three reports to reach that conclusion was sent to Gov. Rick Perry 's office and submitted to appeals courts before Willingham 's execution , while two others were conducted after his death .

`` Despite overwhelming scientific evidence , state officials have continued to demonize Mr. Willingham and defend the arson evidence on which he and others have been convicted , '' the family 's petition states .

The Forensic Science Commission was to hear from the author of the most recent of those reports in October 2009 . But the panel 's deliberations were put off after Perry -- who allowed the execution to go forward -- abruptly shook up the panel , spurring complaints from the Willingham family and allegations that Perry was trying to head off the potential admission that Texas had put an innocent man to death .

In July , the commission found that arson investigators used flawed science but were not negligent and did not commit misconduct .

A spokeswoman for the governor 's office told CNN on Tuesday that Perry , who allowed the execution to go forward , remains convinced of Willingham 's guilt . And Corsicana authorities have said that evidence beyond the testimony of state fire marshals supported Willingham 's conviction .

CNN 's Emanuella Grinberg contributed to this report .

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`` Todd murdered Amber , Karmon and Kameron , '' Stacy Kuykendall says

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Challenge to judge delays new effort to clear dead man 's name

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3 independent reviews have criticized the case against Willingham